Noise parameter determination method

ABSTRACT

According to an aspect of the present description a method for determining selected parameters of a noise characterization equation which describes a noise performance of a device as a function of a controllable variable of the device is provided. The method includes selecting a number of different values of the controllable variable of the device, the number of different values being equal to or larger than the number of parameters that are to be determined; measuring the noise performance of the device for the different values; utilizing the noise characterization equation to set up a number of independent relations which relate the parameters with the measurement results, the number of independent relations being equal to the number of parameters that are to be determined; and determining the parameters from the relations.

BACKGROUND

In the field of wireless communications there is a demand for acontinuous improvement of the sensitivity of the devices. Thesensitivity of a device is typically described with the help of noiseparameters. For example noise figure parameter (NF-parameters) and noisefigure circles (NF-circles) are usually used for an optimum matching ofa low noise amplifier (LNA).

It is therefore a need for an economical method for determining thedesired parameters.

SUMMARY

According to an aspect of the present description a method fordetermining selected parameters of a noise characterization equationwhich describes a noise performance of a device as a function of acontrollable variable relevant to the device is provided. The methodincludes: selecting a number of different values of the controllablevariable relevant to the device, the number of different values beingequal to or larger than the number of parameters that are to bedetermined; measuring the noise performance of the device for thedifferent values; utilizing the noise characterization equation to setup a number of independent relations which relate the parameters withthe measurement results, the number of independent relations being equalto the number of parameters that are to be determined; and determiningthe parameters from the relations.

DRAWINGS

Embodiments are depicted in the drawings and are detailed in thedescription which follows.

In the drawings:

FIG. 1 shows a measurement set-up according to an embodiment of thepresent invention;

FIG. 2 shows a set-up in order to select a desired input impedancevalue;

FIG. 3 shows a measurement set-up according to another embodiment of thepresent invention; and

FIG. 4 shows a set-up in order to select a desired output impedancevalue.

In the figures same reference numerals denote the same or similar partsor steps.

DESCRIPTION

An aspect of the present description is to provide a method to determinethe relevant noise parameters from a comparatively small number ofmeasurement points. In particular, a method is provided for determiningselected parameters of a noise characterization equation which describesa noise performance of a device as a function of a controllable variablerelevant to the device. Preferably, noise characterization equation isexpressed in term of the so called noise figure (NF).

In telecommunication, noise figure (NF) is a measure of degradation ofthe signal to noise ratio (SNR), caused by components in the signalchain. The noise figure is the ratio of the output noise power of adevice to the portion thereof attributable to thermal noise in the inputtermination at standard noise temperature T (usually 290 K). The noisefigure is thus the ratio of actual output noise to that which wouldremain if the device itself did not introduce noise.

Furthermore, the parameters preferably contained in the noisecharacterization equation are the minimum noise figure (NFmin), thecorresponding reflection coefficient or impedance (real part andimaginary part) and the noise resistance.

In the following it is described how a noise characterization equationcan be utilized to set up a number of independent relations which relatethe desired parameters with the measurement results. Preferably, thenoise characterization equation is equivalent to following equation

${\left. 1 \right)\mspace{14mu}{NF}} = {{NF}_{\min} + {\frac{4 \cdot R_{n}}{Z_{0}} \cdot \frac{{{\Gamma_{OPT} - \Gamma_{S}}}^{2}}{{{1 + \Gamma_{OPT}}}^{2} \cdot \left( {1 - {\Gamma_{S}}^{2}} \right)}}}$wherein the parameter NF_(min) denotes the minimum noise figure, theparameter R_(n) denotes the noise resistance, the parameter Γ_(OPT)denotes the optimum reflection coefficient, and the parameter Z₀ denotesa standard impedance. Equation 1) describes the noise figure of a deviceas a function of reflection coefficient Γ_(S). The reflectioncoefficient is a complex number having a real part Γ_(S real) and animaginary part Γ_(S imag). The same applies for parameter Γ_(OPT), whichhas a real part Γ_(OPT real) and an imaginary part Γ_(OPT imag).Thereby, a reflection coefficient can be transformed into acorresponding impedance and vice versa.

From those parameters that appear in equation 1) the minimum noisefigure, the noise resistance and the optimum reflection coefficient areselected so that their respective values can be determined.

For that purpose it is convenient to modify equation 1, so that it takesthe following form:

${\left. 2 \right)\mspace{14mu}{NF}} = {{NF}_{\min} - \frac{4 \cdot R_{n}}{Z_{0} \cdot \left( {1 + {2\Gamma_{{OPT}\mspace{14mu}{real}}} + \Gamma_{{OPT}\mspace{14mu}{real}}^{2} + \Gamma_{{OPT}\mspace{14mu}{imag}}^{2}} \right)} + {{\frac{4 \cdot R_{n}}{Z_{0} \cdot \left( {1 - {\Gamma_{S}}^{2}} \right)}--}{\frac{8 \cdot \left( {1 + \Gamma_{S\mspace{14mu}{real}}} \right)}{Z_{0} \cdot \left( {1 - {\Gamma_{S}}^{2}} \right)} \cdot \frac{\Gamma_{{OPT}\mspace{14mu}{real}} \cdot R_{n}}{Z_{0} \cdot \left( {1 + {2\Gamma_{{OPT}\mspace{14mu}{real}}} + \Gamma_{{OPT}\mspace{14mu}{real}}^{2} + \Gamma_{{OPT}\mspace{14mu}{imag}}^{2}} \right)}}} - {\frac{8 \cdot \Gamma_{S\mspace{14mu}{imag}}}{Z_{0} \cdot \left( {1 - {\Gamma_{S}}^{2}} \right)} \cdot \frac{\Gamma_{{OPT}\mspace{14mu}{imag}} \cdot R_{n}}{Z_{0} \cdot \left( {1 + {2\Gamma_{{OPT}\mspace{14mu}{real}}} + \Gamma_{{OPT}\mspace{14mu}{real}}^{2} + \Gamma_{{OPT}\mspace{14mu}{imag}}^{2}} \right)}}}$

Using the additional variables x₁, x₂, x₃ and x₄:

${\left. {{{\left. {{{\left. {{{\left. \mspace{20mu}{3{a.}} \right)\mspace{14mu} x_{1}} = {{NF}_{\min} - \frac{4 \cdot R_{n}}{Z_{0} \cdot \left( {1 + {2\Gamma_{{OPT}\mspace{14mu}{real}}} + \Gamma_{{OPT}\mspace{14mu}{real}}^{2} + \Gamma_{{OPT}\mspace{14mu}{imag}}^{2}} \right)}}}\mspace{20mu}{3{b.}}} \right)\mspace{14mu} x_{2}} = R_{n}}\mspace{20mu}{3{c.}}} \right){\mspace{11mu}\;}x_{3}} = \frac{\Gamma_{{OPT}\mspace{14mu}{real}} \cdot R_{n}}{Z_{0} \cdot \left( {1 + {2\Gamma_{{OPT}\mspace{11mu}{real}}} + \Gamma_{{OPT}\mspace{11mu}{real}}^{2} + \Gamma_{{OPT}\mspace{11mu}{imag}}^{2}} \right)}}\mspace{20mu}{3{d.}}} \right)\mspace{14mu} x_{4}} = \frac{\Gamma_{{OPT}\mspace{14mu}{imag}} \cdot R_{n}}{Z_{0} \cdot \left( {1 + {2\Gamma_{{OPT}\mspace{14mu}{real}}} + \Gamma_{{OPT}\mspace{14mu}{real}}^{2} + \Gamma_{{OPT}\mspace{14mu}{imag}}^{2}} \right)}$

Equation 2) takes the following form:

${\left. 4. \right)\mspace{14mu}{NF}} = {x_{1} + {\frac{4}{Z_{0} \cdot \left( {1 - {\Gamma_{S}}^{2}} \right)} \cdot x_{2}} - {\frac{8 \cdot \left( {1 + \Gamma_{S\mspace{14mu}{real}}} \right)}{Z_{0} \cdot \left( {1 - {\Gamma_{S}}^{2}} \right)} \cdot x_{3}} - {\frac{8 \cdot \Gamma_{S\mspace{14mu}{imag}}}{Z_{0} \cdot \left( {1 - {\Gamma_{S}}^{2}} \right)} \cdot x_{4}}}$

Equation 4) can also be written as

4b.)  NF_(x) = x₁ + A_(x) ⋅ x₂ + B_(x) ⋅ x₃ + C_(x) ⋅ x₄$\mspace{50mu}{A_{x} = \frac{4}{Z_{0} \cdot \left( {1 - {\Gamma_{Sx}}^{2}} \right)}}$$\mspace{45mu}{B_{x} = {- \frac{8 \cdot \left( {1 + \Gamma_{S\mspace{14mu}{real}\mspace{14mu} x}} \right)}{Z_{0} \cdot \left( {1 - {\Gamma_{Sx}}^{2}} \right)}}}$$\mspace{45mu}{C_{x} = {- \frac{{8 \cdot 1} + \Gamma_{S\mspace{14mu}{imag}\mspace{14mu} x}}{Z_{0} \cdot \left( {1 - {\Gamma_{Sx}}^{2}} \right)}}}$where

To be able to calculate the values of x₁, x₂, x₃ and x₄ and furthermoreΓ_(OPT real), Γ_(OPT imag), Rn and NFmin, at least four different valuesof the reflection coefficient Γ_(S) are selected and the correspondingvalues of the NF are measured. Inserting the measured NF-values and thecorresponding values of Γ_(S) (Γ_(S real) and Γ_(S imag)) in formula 4or 4b yields a system of four independent relations enabling tocalculate the for different values Γ_(OPT real), Γ_(OPT imag), Rn andNFmin by using the additional variables x₁, x₂, x₃ and x₄.

Inserting into 4b yieldsNF ₁ =x ₁ +A ₁ ·x ₂ +B ₁ ·x ₃ +C ₁ ·x ₄  5a.)NF ₂ =x ₁ +A ₂ ·x ₂ +B ₂ ·x ₃ +C ₂ ·x ₄  5b.)NF ₃ =x ₁ +A ₃ ·x ₂ +B ₃ ·x ₃ +C ₃ ·x ₄  5c.)NF ₄ =x ₁ +A ₄ ·x ₂ +B ₄ ·x ₃ +C ₄ ·x ₄  5d.)

Thus relations 5a to 5d relate the desired parameters Γ_(OPT real),Γ_(OPT imag), Rn and NFmin with the measurement results (NF₁ at Γ₁),(NF2 at Γ₂), (NF₃ at Γ₃), and (NF₄ at Γ₄). Solving these relations withregard to by x₁, x₂, x₃ and x₄ yields the following equations:

$\begin{matrix}{{\left. {6{a.}} \right)\mspace{14mu} x_{1}} = \frac{\begin{matrix}{{\xi_{1} \cdot \left( {{\gamma_{2} \cdot \beta_{3}} - {\gamma_{3} \cdot \beta_{2}}} \right)} +} \\{{\xi_{2} \cdot \left( {{\gamma_{3} \cdot \beta_{1}} - {\gamma_{1} \cdot \beta_{3}}} \right)} + {\xi_{3} \cdot \left( {{\gamma_{1} \cdot \beta_{2}} - {\gamma_{2} \cdot \beta_{3}}} \right)}}\end{matrix}}{\begin{matrix}{{\Delta\;{A_{1} \cdot \left( {{\gamma_{2} \cdot \beta_{3}} - {\gamma_{3} \cdot \beta_{2}}} \right)}} +} \\{{\Delta\;{A_{2} \cdot \left( {{\gamma_{3} \cdot \beta_{1}} - {\gamma_{1} \cdot \beta_{3}}} \right)}} + {\Delta\;{A_{3} \cdot \left( {{\gamma_{1} \cdot \beta_{2}} - {\gamma_{2} \cdot \beta_{3}}} \right)}}}\end{matrix}}} \\{\mspace{56mu}{with}} \\{\mspace{59mu}{\xi_{1} = {{F_{1} \cdot A_{2}} - {F_{2} \cdot A_{1}}}}} \\{\mspace{56mu}{\xi_{2} = {{F_{2} \cdot A_{3}} - {F_{3} \cdot A_{2}}}}} \\{\mspace{56mu}{\xi_{3} = {{F_{3} \cdot A_{4}} - {F_{4} \cdot A_{3}}}}} \\{\mspace{56mu}{\beta_{1} = {{B_{1} \cdot A_{2}} - {B_{2} \cdot A_{1}}}}} \\{\mspace{56mu}{\beta_{2} = {{B_{2} \cdot A_{3}} - {B_{3} \cdot A_{2}}}}} \\{\mspace{56mu}{\beta_{3} = {{B_{3} \cdot A_{4}} - {B_{4} \cdot A_{3}}}}} \\{\mspace{56mu}{\gamma_{1} = {{C_{1} \cdot A_{2}} - {C_{2} \cdot A_{1}}}}} \\{\mspace{56mu}{\gamma_{2} = {{C_{2} \cdot A_{3}} - {C_{3} \cdot A_{2}}}}} \\{\mspace{56mu}{\gamma_{3} = {{C_{3} \cdot A_{4}} - {C_{4} \cdot A_{3}}}}} \\{\mspace{56mu}{{\Delta\; A_{1}} = {A_{2} - A_{1}}}} \\{\mspace{56mu}{{\Delta\; A_{2}} = {A_{3} - A_{2}}}} \\{\mspace{56mu}{{\Delta\; A_{3}} = {A_{4} - A_{3}}}} \\\begin{matrix}{{\left. {6{b.}} \right)\mspace{14mu} x_{2}} = \frac{\begin{matrix}{{\left( {{NF}_{1} - {NF}_{2}} \right) \cdot \begin{bmatrix}{{\left( {C_{2} - C_{3}} \right) \cdot \left( {B_{3} - C_{4}} \right)} -} \\{\left( {C_{3} - C_{4}} \right) \cdot \left( {B_{2} - B_{3}} \right)}\end{bmatrix}} +} \\{{\left( {{NF}_{2} - {NF}_{3}} \right) \cdot \begin{bmatrix}{{\left( {C_{3} - C_{4}} \right) \cdot \left( {B_{1} - B_{2}} \right)} -} \\{\left( {C_{1} - C_{2}} \right) \cdot \left( {B_{3} - B_{4}} \right)}\end{bmatrix}} +} \\{{\left( {{NF}_{3} - {NF}_{4}} \right) \cdot \begin{bmatrix}{{\left( {C_{1} - C_{2}} \right) \cdot \left( {B_{2} - B_{3}} \right)} -} \\{\left( {C_{2} - C_{3}} \right) \cdot \left( {B_{1} - B_{2}} \right)}\end{bmatrix}}\mspace{14mu}}\end{matrix}}{\begin{matrix}{{\left( {A_{1} - A_{2}} \right) \cdot \begin{bmatrix}{{\left( {C_{2} - C_{3}} \right) \cdot \left( {B_{3} - C_{4}} \right)} -} \\{\left( {C_{3} - C_{4}} \right) \cdot \left( {B_{2} - B_{3}} \right)}\end{bmatrix}} +} \\{{\left( {A_{2} - A_{3}} \right) \cdot \begin{bmatrix}{{\left( {C_{3} - C_{4}} \right) \cdot \left( {B_{1} - B_{2}} \right)} -} \\{\left( {C_{1} - C_{2}} \right) \cdot \left( {B_{3} - B_{4}} \right)}\end{bmatrix}} +} \\{{\left( {A_{3} - A_{4}} \right) \cdot \begin{bmatrix}{{\left( {C_{1} - C_{2}} \right) \cdot \left( {B_{2} - B_{3}} \right)} -} \\{\left( {C_{2} - C_{3}} \right) \cdot \left( {B_{1} - B_{2}} \right)}\end{bmatrix}}\mspace{11mu}}\end{matrix}}} \\{{\left. {6{c.}} \right)\mspace{25mu} x_{3}} = \frac{\begin{matrix}{{\left( {{NF}_{1} - {NF}_{2}} \right) \cdot \begin{bmatrix}{{\left( {C_{2} - C_{3}} \right) \cdot \left( {B_{3} - C_{4}} \right)} -} \\{\left( {C_{3} - C_{4}} \right) \cdot \left( {B_{2} - B_{3}} \right)}\end{bmatrix}} +} \\{{\left( {{NF}_{2} - {NF}_{3}} \right) \cdot \begin{bmatrix}{{\left( {C_{3} - C_{4}} \right) \cdot \left( {B_{1} - B_{2}} \right)} -} \\{\left( {C_{1} - C_{2}} \right) \cdot \left( {B_{3} - B_{4}} \right)}\end{bmatrix}} +} \\{\left( {{NF}_{3} - {NF}_{4}} \right) \cdot \begin{bmatrix}{{\left( {C_{1} - C_{2}} \right) \cdot \left( {B_{2} - B_{3}} \right)} -} \\{\left( {C_{2} - C_{3}} \right) \cdot \left( {B_{1} - B_{2}} \right)}\end{bmatrix}}\end{matrix}}{\begin{matrix}{{\left( {B_{1} - B_{2}} \right) \cdot \begin{bmatrix}{{\left( {C_{2} - C_{3}} \right) \cdot \left( {B_{3} - C_{4}} \right)} -} \\{\left( {C_{3} - C_{4}} \right) \cdot \left( {B_{2} - B_{3}} \right)}\end{bmatrix}} +} \\{{\left( {B_{2} - B_{3}} \right) \cdot \begin{bmatrix}{{\left( {C_{3} - C_{4}} \right) \cdot \left( {B_{1} - B_{2}} \right)} -} \\{\left( {C_{1} - C_{2}} \right) \cdot \left( {B_{3} - B_{4}} \right)}\end{bmatrix}} +} \\{{\left( {B_{3} - B_{4}} \right) \cdot \begin{bmatrix}{{\left( {C_{1} - C_{2}} \right) \cdot \left( {B_{2} - B_{3}} \right)} -} \\{\left( {C_{2} - C_{3}} \right) \cdot \left( {B_{1} - B_{2}} \right)}\end{bmatrix}}\mspace{14mu}}\end{matrix}}} \\{{\left. {6{d.}} \right)\mspace{25mu} x_{4}} = \frac{\begin{matrix}{{\left( {{NF}_{1} - {NF}_{2}} \right) \cdot \begin{bmatrix}{{\left( {C_{2} - C_{3}} \right) \cdot \left( {B_{3} - C_{4}} \right)} -} \\{\left( {C_{3} - C_{4}} \right) \cdot \left( {B_{2} - B_{3}} \right)}\end{bmatrix}} +} \\{{\left( {{NF}_{2} - {NF}_{3}} \right) \cdot \begin{bmatrix}{{\left( {C_{3} - C_{4}} \right) \cdot \left( {B_{1} - B_{2}} \right)} -} \\{\left( {C_{1} - C_{2}} \right) \cdot \left( {B_{3} - B_{4}} \right)}\end{bmatrix}} +} \\{\left( {{NF}_{3} - {NF}_{4}} \right) \cdot \begin{bmatrix}{{\left( {C_{1} - C_{2}} \right) \cdot \left( {B_{2} - B_{3}} \right)} -} \\{\left( {C_{2} - C_{3}} \right) \cdot \left( {B_{1} - B_{2}} \right)}\end{bmatrix}}\end{matrix}}{\begin{matrix}{{\left( {C_{1} - C_{2}} \right) \cdot \begin{bmatrix}{{\left( {C_{2} - C_{3}} \right) \cdot \left( {B_{3} - C_{4}} \right)} -} \\{\left( {C_{3} - C_{4}} \right) \cdot \left( {B_{2} - B_{3}} \right)}\end{bmatrix}} +} \\{{\left( {C_{2} - C_{3}} \right) \cdot \begin{bmatrix}{{\left( {C_{3} - C_{4}} \right) \cdot \left( {B_{1} - B_{2}} \right)} -} \\{\left( {C_{1} - C_{2}} \right) \cdot \left( {B_{3} - B_{4}} \right)}\end{bmatrix}} +} \\{{\left( {C_{3} - C_{4}} \right) \cdot \begin{bmatrix}{{\left( {C_{1} - C_{2}} \right) \cdot \left( {B_{2} - B_{3}} \right)} -} \\{\left( {C_{2} - C_{3}} \right) \cdot \left( {B_{1} - B_{2}} \right)}\end{bmatrix}}\mspace{14mu}}\end{matrix}}}\end{matrix}\end{matrix}$

After having calculated x₁, x₂, x₃ and x₄ finally Γ_(OPT real),Γ_(OPT imag), Rn and NFmin can be calculated as follows:

${\left. {{{\left. {{\left. {{{\left. 7. \right)\mspace{14mu}\Gamma_{{OPT}\mspace{14mu}{real}}} = {\left( \frac{x_{3}}{x_{2}} \right) \cdot \frac{1 - {{2 \cdot \frac{x_{3}}{x_{2}}}( + )} - \sqrt{1 - {4 \cdot \frac{x_{3}}{x_{2}}} - {4 \cdot \left( \frac{x_{4}}{x_{2}} \right)^{2}}}}{2 \cdot \left\lbrack {\left( \frac{x_{3}}{x_{2}} \right)^{2} + \left( \frac{x_{4}}{x_{2}} \right)^{2}} \right\rbrack}}}8.} \right)\mspace{14mu}\begin{matrix}{\Gamma_{{OPT}\mspace{14mu}{imag}} = {\left( \frac{x_{4}}{x_{2}} \right) \cdot \frac{1 - {{2 \cdot \frac{x_{3}}{x_{2}}}( + )} - \sqrt{1 - {4 \cdot \frac{x_{3}}{x_{2}}} - {4 \cdot \left( \frac{x_{4}}{x_{2}} \right)^{2}}}}{2 \cdot \left\lbrack {\left( \frac{x_{3}}{x_{2}} \right)^{2} + \left( \frac{x_{4}}{x_{2}} \right)^{2}} \right\rbrack}}} \\{= {\frac{x_{4}}{x_{2}} \cdot \Gamma_{{OPT}\mspace{14mu}{imag}}}}\end{matrix}}9.} \right)\mspace{25mu} R_{n}} = x_{2}}\mspace{59mu}{and}10.} \right)\mspace{14mu}{NF}_{\min}} = {x_{1} + {\cdot \frac{8 \cdot \left( {x_{3}^{2} + x_{4}^{2}} \right) \cdot \frac{1}{x_{2}}}{Z_{0} \cdot \left( {1 - {{2 \cdot \frac{x_{3}}{x_{2}}}( + )} - \sqrt{1 - {4 \cdot \frac{x_{3}}{x_{2}}} - {4 \cdot \left( \frac{x_{4}}{x_{2}} \right)^{2}}}} \right)}}}$

As outlined above, in the present example only four NF-measurements arenecessary to determine the desired NF-parameters from equation 1. As theparameter Γ_(OPT) is found by calculation using exact formulas from fourmeasurements at different reflections coefficients, instead ofapproximation by searching Γ_(OPT) (where the accuracy is dependent onthe step size and therefore on the amount of measurements), the accuracyof the value of the parameter Γ_(OPT) is high. Furthermore measurementpoints showing sufficient gain can be chosen to keep the influence ofthe measurement device sufficiently small.

As a numerical example a measurement using four reflection coefficientsor impedance values was performed:

-   -   a. Γ₁=0.2+j0=>NF₁=2.1    -   b. Γ₂=0.2+j0.5=>NF₂=2.2    -   c. Γ₃=−0.1−j0.3=>NF₃=3.2    -   d. Γ₄=0.5+j0.6=>NF₄=2.4        yields the following noise parameter:    -   e. NFmin=1,803=2,559 dB    -   f. Rn=54,9563Ω    -   g. Γ_(OPT)=0.492099+j0.2517460

In addition to noise parameters noise figure circles may also be used todescribe the noise behavior of a device. The noise figure circles arenon concentric circles in the Smith-Chart characterized by the same NFof all points on the respective circle and the reflection coefficient ofthe optimum NF anywhere in the center of these circles. So for example,beside the reflection coefficient of the optimum NF, circles showing a0.5 dB, 1 dB, 1.5 dB . . . larger NF than the optimum NF can be insertedand displayed in the Smith-Chart.

The NF-circles are calculated by derive both the x-value and the y-valueof Γ_(S) of points of the circle from formula 1. For that purpose oncethe x-value of Γ_(OPT) has to be inserted as x-value of Γ_(S) (and ofcourse Γ_(OPT) and Fmin) into this formula, to get the correspondingy-values of Γ_(S) and once to insert the y-value of Γ_(OPT) as y-valueof Γ_(S) (and of course Γ_(OPT) and Fmin) into this formula, to get thex-values of Γ_(S).

For the noise characterization equation 1) it can be shown that the fourmeasurements points (reflection coefficients) must not lie on one andthe same line or on one and the same circle in the Smith-Diagram. Ifthis would be the case no solution of the equation system 5a to 5d wouldbe possible. Therefore, it is helpful when a check is performed whetherthe selected impedance values yield a sufficient number of independentrelations which relate the parameters with the measurement results.

In order to avoid measurements that may then not be usable for thedetermination of the desired parameters, it is also helpful to select anumber of different impedance values of the device, the number ofdifferent impedance values being less than the number of parameters thatare to be determined. Based on the selected impedance values thosevalues for the remaining impedance points, that are not to be selected,are determined.

In the above described example three impedance values were selected andthe forbidden coordinates of the fourth measurement point weredetermined. The line or circle representing the forbidden reflectioncoefficient for the fourth measurement may, for example, be indicated ina corresponding Smith-Diagram. In addition the forbidden imaginary valueof this point may be indicated as warning after the real value of thethis point has been selected.

One possibility to measure the noise figure NF at a certain inputimpedance is described with reference to FIG. 1. In FIG. 1 the devicewhose noise performance is to be determined is illustrated at referencenumber 30. A noise source 10 is used to supply a noise signal to theinput of the device under test (DUT) 30 via a stub tuner 24. The stubtuner 24 is used to adjust the impedance as seen at the input of thedevice under test 30. Accordingly, the stub tuner 24 is used to selectdifferent input impedance values of the device under test 30. On theoutput of the device under test 30 a noise figure meter 40 is used tomeasure the noise figure of the device 30 for the different inputimpedance values.

To adjust the input impedance of the device 30 present on the output 2of the stub tuner 24 to a desired value a network analyser (NA) 50 isused, as can be seen FIG. 2. The input port 1 of the stub tuner 24 canbe terminated either by a 50Ω termination or connected to acorresponding port of the network analyser 50. The stub tuner 24includes one or more short-circuited, variable length lines (stubs)connected to the primary transmission line reaching from the input port1 to the output port 2. Thereby each stub is movable over a certainrange, in order to adjust a desired impedance value. Once the desiredimpedance value is measured by the network analyzer 50, thecorresponding stub positions are fixed and the stub tuner 24 isreconnected with the input of the device under test 30.

In order to increase the accuracy of the measurement, it is preferredthat the output impedance of the device under test is transformed to50Ω. Thus, as can be seen from FIG. 3, the output of the device undertest 30 is connected to the input port 1 of a second stub tuner 25. Thetransformation of the DUT output impedance to 50Ω helps to reach ahigher accuracy, as the calibration of the noise figure meter 40 istypically related to the 50Ω impedance of the noise source 10.

The stubs of the stub tuner 25 can be adjusted by measuring directly onthe output 2 of the second stub tuner 25 using the network analyzer 50until 50Ω is reached (FIG. 4). Afterwards the output 2 of the secondstub tuner 25 is connected to the measuring input of the noise figuremeter 40 to measure the NF of the device under test at this particularinput impedance.

The measurement result achieved in the described manner represents thesystem noise figure including, in addition to the device under test 30,also the first and second stub tuner 24 and 25 and additional cables,which were not used during the calibration of the noise figure meter 40.Thus this value has to be corrected by using the Friis-formula with theknown noise figure of each additional component, namely the first andsecond stub tuners 24 and 25 and additional cables.

Based on the measured values the noise parameters of the device undertest can be determined. These noise parameters may then be used tochance certain properties of the device under test itself or to designcorresponding matching networks used for example at the input of thedevice under test such that the overall the sensitivity requirements canbe met.

1. A method for determining selected parameters of a noisecharacterization equation which describes a noise performance of adevice as a function of a controllable variable relevant to the device,comprising: selecting, by a stub tuner, a number of different values ofthe controllable variable relevant to the device, the number ofdifferent values being equal to or larger than the number of parametersthat are to be determined; measuring, by a noise figure meter, the noiseperformance of the device for the different values; utilizing the noisecharacterization equation to set up a number of independent relationswhich relate the parameters with the measurement results, the number ofindependent relations being equal to the number of parameters that areto be determined; determining the parameters from the relations; andutilizing the noise characterization equation with the determinedparameters to improve the noise performance of the device.
 2. The methodaccording to claim 1, wherein the controllable variable is an impedancerelevant to the device.
 3. The method according to claim 2, wherein thenoise characterization equation describes a noise performance of thedevice as a function of input impedance relevant to the device.
 4. Themethod according to claim 1, wherein noise performance is given in aform of a noise figure.
 5. The method according to claim 1, wherein theselected parameters include a minimum noise figure.
 6. The methodaccording to claim 1, wherein the selected parameters include noiseresistance.
 7. The method according to claim 1, wherein the selectedparameters include optimum impedance.
 8. The method according to claim1, wherein the noise characterization equation is equivalent to:${NF} = {{NF}_{\min} + {\frac{4 \cdot R_{n}}{Z_{0}} \cdot {\frac{{{\Gamma_{OPT} - \Gamma_{S}}}^{2}}{{{1 + \Gamma_{OPT}}}^{2} \cdot \left( {1 - {\Gamma_{S}}^{2}} \right)}.}}}$wherein the parameter NF_(min) denotes a minimum noise figure, theparameter R_(n) denotes noise resistance, the parameter Γ_(OPT) denotesoptimum reflection coefficient, and the parameter Z₀ denotes a standardimpedance.
 9. The method according to claim 1, wherein the relationswhich relate the parameters with the measurement results are in equationform.
 10. The method according to claim 1, further comprising: checkingwhether the selected values yield a sufficient number of independentrelations which relate the parameters with the measurement results. 11.The method according to claim 1, further comprising: selecting, by thestub tuner, a number of different values of the controllable variablerelevant to the device, the number of different values being less thanthe number of parameters that are to be determined; and determiningbased on the selected values, those values of the remaining values thatshould not be selected.